The new Prime Minister said the scheme will "get everyone in for Christmas" with emergency accommodation and help rolled out in England later this year.
Downing Street said under the support - backed by £442million - areas with the greatest need will receive the largest share in order to get people out of the cold in winter.
Mr Burnham will also convene a "first of its kind" national summit in the autumn months on ending rough sleeping, officials added. They said it would bring together leaders from business, finance, health and faith communities to ask how they can all play a role.
